# EmpiricalMV: EmpiricalMV Distribution Class In distr6: The Complete R6 Probability Distributions Interface

## Description

Mathematical and statistical functions for the EmpiricalMV distribution, which is commonly used in sampling such as MCMC.

## Details

The EmpiricalMV distribution is defined by the pmf,

p(x) = ∑ I(x = x_i) / k

for x_i ε R, i = 1,...,k.

Sampling from this distribution is performed with the sample function with the elements given as the support set and uniform probabilities. Sampling is performed with replacement, which is consistent with other distributions but non-standard for Empirical distributions. Use simulateEmpiricalDistribution to sample without replacement.

The cdf assumes that the elements are supplied in an indexed order (otherwise the results are meaningless).

## Value

Returns an R6 object inheriting from class SDistribution.

## Distribution support

The distribution is supported on x_1,...,x_k.

## Default Parameterisation

EmpMV(data = data.frame(1, 1))

N/A

N/A

## Super classes

`distr6::Distribution` -> `distr6::SDistribution` -> `EmpiricalMV`

## Public fields

`name`

Full name of distribution.

`short_name`

Short name of distribution for printing.

`description`

Brief description of the distribution.

## Methods

#### Public methods

Inherited methods

#### Method `new()`

Creates a new instance of this R6 class.

##### Usage
`EmpiricalMV\$new(data = NULL, decorators = NULL)`
##### Arguments
`data`

`[matrix]`
Matrix-like object where each column is a vector of observed samples corresponding to each variable.

`decorators`

`(character())`
Decorators to add to the distribution during construction.

##### Examples
```EmpiricalMV\$new(MultivariateNormal\$new()\$rand(100))
```

#### Method `mean()`

The arithmetic mean of a (discrete) probability distribution X is the expectation

E_X(X) = ∑ p_X(x)*x

with an integration analogue for continuous distributions.

##### Usage
`EmpiricalMV\$mean(...)`
`...`

Unused.

#### Method `variance()`

The variance of a distribution is defined by the formula

var_X = E[X^2] - E[X]^2

where E_X is the expectation of distribution X. If the distribution is multivariate the covariance matrix is returned.

##### Usage
`EmpiricalMV\$variance(...)`
`...`

Unused.

#### Method `setParameterValue()`

Sets the value(s) of the given parameter(s).

##### Usage
```EmpiricalMV\$setParameterValue(
...,
lst = NULL,
error = "warn",
resolveConflicts = FALSE
)```
##### Arguments
`...`

`ANY`
Named arguments of parameters to set values for. See examples.

`lst`

`(list(1))`
Alternative argument for passing parameters. List names should be parameter names and list values are the new values to set.

`error`

`(character(1))`
If `"warn"` then returns a warning on error, otherwise breaks if `"stop"`.

`resolveConflicts`

`(logical(1))`
If `FALSE` (default) throws error if conflicting parameterisations are provided, otherwise automatically resolves them by removing all conflicting parameters.

#### Method `clone()`

The objects of this class are cloneable with this method.

##### Usage
`EmpiricalMV\$clone(deep = FALSE)`
##### Arguments
`deep`

Whether to make a deep clone.

## References

McLaughlin, M. P. (2001). A compendium of common probability distributions (pp. 2014-01). Michael P. McLaughlin.

Other discrete distributions: `Bernoulli`, `Binomial`, `Categorical`, `Degenerate`, `DiscreteUniform`, `Empirical`, `Geometric`, `Hypergeometric`, `Logarithmic`, `Multinomial`, `NegativeBinomial`, `WeightedDiscrete`
Other multivariate distributions: `Dirichlet`, `Multinomial`, `MultivariateNormal`
 ```1 2 3 4 5``` ```## ------------------------------------------------ ## Method `EmpiricalMV\$new` ## ------------------------------------------------ EmpiricalMV\$new(MultivariateNormal\$new()\$rand(100)) ```